This invention relates to the field of optical angular rate sensors of the passive ring resonator type typified in Lawrence U.S. Pat. No. 4,326,803. In such an instrument a passive waveguide provides a closed loop propagation path for optical signals about a measurement axis. Coherent optical signals are coupled into the path for propagation in opposite directions therearound: as pointed out by Sagnac, the effective length of this path varies with the direction and rate of the rotation of the instrument about the measurement axis. The frequencies of the oppositely propagating signals are adjusted to make them resonant in the propagation path, and output coupling means samples the two frequencies, maintains them at resonant values, and determines their difference as a measure of the rate of rotation of the instrument.